A Kent police spokesperson told media on Friday they "can confirm an ongoing investigation into the supply of drugs in connection with the death of Peaches Geldof," according to THR. "There have been no arrests at this stage."

On Thursday, it was confirmed that drugs played a part in her shocking and untimely death. "Recent use of heroin and the levels identified were likely to have played a role in her death," Detective Chief Inspector Paul Fotheringham of the Kent and Essex Serious Crime Directorate said in a hearing.

Geldof was discovered dead in her Kent home on Monday, Apr. 7. She was home alone with her 11-month-old son Phaedra. Geldof is survived by husband Thomas Cohen, Phaedra and their other son Astala.

At the time of her death, Cohen released a heartbreaking statement, saying, "My beloved wife Peaches was adored by myself and her two sons Astala and Phaedra and I shall bring them up with their mother in their hearts everyday. We shall love her forever."

Geldof was the daughter if Irish musician Bob Geldof and British TV personality Paula Yates. Eerily, Yates died of an accidental heroin overdose in 2000 at only 41 years old.